Show the Proof

import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof

	step type	requirements	statement
0	instantiation	1, 2, 3, 4, 5	,  ⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.number_sets.real_numbers.in_IntervalCO
2	reference	33	⊢
3	reference	50	⊢
4	reference	69	⊢
5	instantiation	6, 7, 8	,  ⊢
	: , :
6	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
7	instantiation	23, 80, 33, 24, 9, 27, 10*, 28*	,  ⊢
	: , : , :
8	instantiation	11, 12, 13	,  ⊢
	: , : , :
9	instantiation	14, 74, 75, 63	,  ⊢
	: , : , :
10	instantiation	15, 68, 47	⊢
	:
11	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
12	instantiation	16, 17, 18	,  ⊢
	: , : , :
13	instantiation	19, 50, 20, 33, 21, 22*	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
15	theorem		⊢
	proveit.numbers.division.frac_zero_numer
16	theorem		⊢
	proveit.logic.equality.sub_right_side_into
17	instantiation	23, 80, 24, 25, 26, 27, 28*	,  ⊢
	: , : , :
18	instantiation	29, 68, 38, 47, 30*	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.addition.strong_bound_via_right_term_bound
20	instantiation	31, 34	⊢
	:
21	instantiation	32, 33, 34, 35, 36*	⊢
	: , :
22	instantiation	37, 38	⊢
	:
23	theorem		⊢
	proveit.numbers.division.weak_div_from_numer_bound__pos_denom
24	instantiation	109, 92, 39	,  ⊢
	: , : , :
25	instantiation	109, 92, 40	⊢
	: , : , :
26	instantiation	41, 74, 75, 63	,  ⊢
	: , : , :
27	instantiation	42, 97	⊢
	:
28	instantiation	43, 44, 45	,  ⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.division.distribute_frac_through_subtract
30	instantiation	46, 68, 47	⊢
	:
31	theorem		⊢
	proveit.numbers.negation.real_closure
32	theorem		⊢
	proveit.numbers.negation.negated_strong_bound
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
34	instantiation	109, 92, 48	⊢
	: , : , :
35	instantiation	49, 60	⊢
	:
36	theorem		⊢
	proveit.numbers.negation.negated_zero
37	theorem		⊢
	proveit.numbers.addition.elim_zero_right
38	instantiation	109, 79, 50	⊢
	: , : , :
39	instantiation	109, 100, 51	,  ⊢
	: , : , :
40	instantiation	109, 100, 75	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
42	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
43	axiom		⊢
	proveit.logic.equality.equals_transitivity
44	instantiation	52, 53, 54, 57, 55*	,  ⊢
	: , : , :
45	instantiation	56, 57	⊢
	:
46	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
47	instantiation	58, 97	⊢
	:
48	instantiation	109, 59, 60	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
50	instantiation	109, 92, 61	⊢
	: , : , :
51	instantiation	109, 62, 63	,  ⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.division.frac_cancel_left
53	instantiation	109, 65, 64	⊢
	: , : , :
54	instantiation	109, 65, 66	⊢
	: , : , :
55	instantiation	67, 68	⊢
	:
56	theorem		⊢
	proveit.numbers.division.frac_one_denom
57	instantiation	109, 79, 69	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
59	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
60	instantiation	70, 71, 72	⊢
	: , :
61	instantiation	109, 100, 96	⊢
	: , : , :
62	instantiation	73, 74, 75	⊢
	: , :
63	instantiation	81, 102, 85	⊢
	: , : , : , : , :
64	instantiation	109, 77, 76	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
66	instantiation	109, 77, 78	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
68	instantiation	109, 79, 80	⊢
	: , : , :
69	instantiation	81, 82, 108, 83, 84, 85	⊢
	: , : , : , : , :
70	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
71	instantiation	109, 86, 99	⊢
	: , : , :
72	instantiation	109, 86, 97	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
74	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
75	instantiation	87, 101, 88	⊢
	: , :
76	instantiation	109, 90, 89	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
78	instantiation	109, 90, 91	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
80	instantiation	109, 92, 93	⊢
	: , : , :
81	theorem		⊢
	proveit.logic.booleans.conjunction.any_from_and
82	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
83	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
84	instantiation	94	⊢
	: , :
85	assumption		⊢
86	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
87	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
88	instantiation	95, 96	⊢
	:
89	instantiation	109, 98, 97	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
91	instantiation	109, 98, 99	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
93	instantiation	109, 100, 101	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
95	theorem		⊢
	proveit.numbers.negation.int_closure
96	instantiation	109, 107, 102	⊢
	: , : , :
97	instantiation	103, 108, 106	⊢
	: , :
98	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
99	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
100	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
101	instantiation	104, 105, 106	⊢
	: , :
102	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
103	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
104	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
105	instantiation	109, 107, 108	⊢
	: , : , :
106	instantiation	109, 110, 111	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
108	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
109	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
110	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
111	assumption		⊢
*equality replacement requirements